Abstract: It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

Stephan TillmannAffiliation:
Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
Email:
tillmann@ms.unimelb.edu.au

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09387-8
PII:
S 0002-9939(08)09387-8
Keywords:
Hyperbolic manifold,
ideal triangulation,
partially truncated triangulation,
subgroup separability
Received by editor(s):
April 9, 2007
Published electronically:
March 10, 2008
Additional Notes:
The research of the first author was supported in part by the NSF
The second author was partly supported by the NSF (DMS-0508971).
The third author was supported under the Australian Research Council’s Discovery funding scheme (project number DP0664276).
This work is in the public domain.
Communicated by:
Daniel Ruberman